Interval of Convergence


#1

The power series for \frac{1}{1-x} is \sum_0^\infty x^{n} for |x|<1.
We can use this to create the power series for arctan(x), by substituting -x^{2} for x and integrating.

We get: arctan(x) = \sum_0^\infty (-1)^{n}\frac{x^{2n+1}}{2n+1} . The interval of convergence of arctan(x) is similar to that of \frac{1}{1-x}. However, I am unsure if the series for arctan(x) converges for x = -1 and x = 1. Can you assist me?